What is the integral of e^8xcos(x) ?

The integral of e^8xcos(x) is e^8(xsin(x)+cos(x))+C

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integral of e^8xcos(x)

integral

e^{8} x cos (x)

e^{8} (x sin (x) + cos (x)) + C

Solution steps

\int e^{8} x cos (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= e^{8} \cdot \int x cos (x) d x

Apply Integration By Parts

: x sin (x) - \int sin (x) d x

= e^{8} (x sin (x) - \int sin (x) d x)

\int sin (x) d x = - cos (x)

= e^{8} (x sin (x) - (- cos (x)))

Simplify

= e^{8} (x sin (x) + cos (x))

Add a constant to the solution

= e^{8} (x sin (x) + cos (x)) + C

(5 - 3 x) (2 + x^{2})

(d^{4} - 2 d^{2} + 1) y = cos (x)

(d^{2} - 4 d + 4) y = e^{2 x} + cos (2 x) + x^{3}

(d^{2} - 9) y = e^{3} x + e^{- 3} x

(d^{4} - 1) y = sin (x)

What is the integral of e^8xcos(x) ?
The integral of e^8xcos(x) is e^8(xsin(x)+cos(x))+C